Positioning devices for purposes of fluid injection are known from the related art, in varying embodiments having needle-shaped positioning elements, which are operated with the aid of a ceramic piezoelectric actuator in order to perform rapid injections of fluid. A particular disadvantage of such devices is that as a result of the characteristic degradation of the piezoelectric actuators as a function of the number of electric cycles, it is not possible to establish a direct correlation between the voltage applied and the expansion of the piezoelectric actuator. This means that the actual position of the positioning element cannot be determined exactly at any point in time of the injection process. In addition, every individual piezoelectric actuator has to be measured and coded in the manufacturing process, which is time-consuming and costly, in order to ascertain the individual lifting capacity for metering the fluid.